A library has 5000 books, and the librarian wants to encode each using a code- word consisting of 3 letters followed by 3 numbers. Are there enough codewords to encode all 5000 with different codewords?

Algebra and Trigonometry (MindTap Course List)
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ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CT: Chapter Test
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10. A library has 5000 books, and the librarian wants to encode each using a code-
word consisting of 3 letters followed by 3 numbers. Are there enough codewords
to encode all 5000 with different codewords?
11. Suppose we want to build a trinary code for the 26 letters of the alphabet, using
strings in which each symbol is 0,1, or -1.
(a) Could we encode all 26 letters using strings of length at most 2?
(b) What about using strings of length exactly 3?
(c) Compute the maximum number of strings of length exactly 4.
(d) Repeat for length exactly 4, but beginning with 0 or 1.
Transcribed Image Text:10. A library has 5000 books, and the librarian wants to encode each using a code- word consisting of 3 letters followed by 3 numbers. Are there enough codewords to encode all 5000 with different codewords? 11. Suppose we want to build a trinary code for the 26 letters of the alphabet, using strings in which each symbol is 0,1, or -1. (a) Could we encode all 26 letters using strings of length at most 2? (b) What about using strings of length exactly 3? (c) Compute the maximum number of strings of length exactly 4. (d) Repeat for length exactly 4, but beginning with 0 or 1.
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